How many triangles can be formed by joining any 3 of the 9 points when

i) no 3 of them  are collinear?

ii) 5 of them are collinear?

 

Asked by kandappan | 10th Feb, 2020, 05:34: PM

Expert Answer:

i.

Number of triangles that can be formed by joining

any three of the 9 points when no three of them are collinear

begin mathsize 16px style straight C presuperscript 9 subscript 3 end style

begin mathsize 16px style equals fraction numerator 9 factorial over denominator open parentheses 9 minus 6 close parentheses factorial 6 factorial end fraction
equals fraction numerator 9 cross times 8 cross times 7 cross times 6 factorial over denominator 6 factorial cross times 3 cross times 2 end fraction
equals 84
end style

ii. 

Number of triangles that can be formed by joining

any three of the 9 points when 5 of them are collinear

begin mathsize 16px style straight C presuperscript 9 subscript 3 space minus space straight C presuperscript 5 subscript 3
equals space 84 space minus space 10
equals space 74 end style

 

Answered by Yasmeen Khan | 10th Feb, 2020, 05:51: PM